# Precalculus Examples

Step 1

Consider the corresponding sign chart.

Step 2

Calculate the minor for element .

Consider the determinant with the row and column deleted.

Evaluate the determinant.

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Subtract from .

Calculate the minor for element .

Consider the determinant with the row and column deleted.

Evaluate the determinant.

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Subtract from .

Calculate the minor for element .

Consider the determinant with the row and column deleted.

Evaluate the determinant.

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Subtract from .

Calculate the minor for element .

Consider the determinant with the row and column deleted.

Evaluate the determinant.

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Subtract from .

Calculate the minor for element .

Consider the determinant with the row and column deleted.

Evaluate the determinant.

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Subtract from .

Calculate the minor for element .

Consider the determinant with the row and column deleted.

Evaluate the determinant.

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Subtract from .

Calculate the minor for element .

Consider the determinant with the row and column deleted.

Evaluate the determinant.

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Subtract from .

Calculate the minor for element .

Consider the determinant with the row and column deleted.

Evaluate the determinant.

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Subtract from .

Calculate the minor for element .

Consider the determinant with the row and column deleted.

Evaluate the determinant.

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Subtract from .

The cofactor matrix is a matrix of the minors with the sign changed for the elements in the positions on the sign chart.

Step 3

Transpose the matrix by switching its rows to columns.